UNIT 5
Study Guide
MODULE
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10
Review
Random Samples and
Populations
ESSENTIAL QUESTION
How can you use random samples and populations to solve
real-world problems?
Key Vocabulary
biased sample (muestra
sesgada)
population (población)
random sample (muestra
aleatoria)
sample (muestra)
EXAMPLE 1
An engineer at a lightbulb factory chooses a random sample of 100
lightbulbs from a shipment of 2,500 and finds that 2 of them are
defective. How many lightbulbs in the shipment are likely to be defective?
defective lightbulbs
defective lightbulbs in population
_______________
= _________________________
size of sample
size of population
2
x
___ = ____
100
2,500
2 · 25
x
______
____
= 2,500
100 · 25
x = 50
In a shipment of 2,500 lightbulbs, 50 are likely to be defective.
EXAMPLE 2
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The 300 students in a school are about to vote for student body
president. There are two candidates, Jay and Serena, and each
candidate has about the same amount of support. Use a simulation
to generate a random sample. Interpret the results.
Step 1: Write the digits 0 through 9 on 10 index cards, one digit per card.
Draw and replace a card three times to form a 3-digit number. For
example, if you draw 0-4-9, the number is 49. If you draw 1-0-8,
the number is 108. Repeat this process until you have a sample of
30 3-digit numbers.
Step 2: Let the numbers from 1 to 150 represent votes for Jay and the numbers
from 151 to 300 represent votes for Serena. For example:
Jay: 83, 37, 16, 4, 127, 93, 9, 62, 91, 75, 13, 35, 94, 26, 60, 120, 36, 73
Serena: 217, 292, 252, 186, 296, 218, 284, 278, 209, 296, 190, 300
Step 3: Notice that 18 of the 30 numbers represent votes for Jay. The results
18
suggest that Jay will receive __
= 60% of the 300 votes, or 180 votes.
30
Step 4: Based on this one sample, Jay will win the election. The results of
samples can vary. Repeating the simulation many times and looking at
the pattern across the different samples will produce more reliable results.
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EXERCISES
1. Molly uses the school directory to select, at random, 25 students
from her school for a survey on which sports people like to watch
on television. She calls the students and asks them, “Do you think
basketball is the best sport to watch on television?” (Lesson 10.1)
a. Did Molly survey a random sample or a biased sample of the
students at her school?
b. Was the question she asked an unbiased question? Explain your
answer.
2. There are 2,300 licensed dogs in Clarkson. A random sample of
50 of the dogs in Clarkson shows that 8 have ID microchips
implanted. How many dogs in Clarkson are likely to have ID
microchips implanted? (Lesson 10.2)
3. A store gets a shipment of 500 MP3 players. Twenty-five of the
players are defective, and the rest are working. A graphing calculator
is used to generate 20 random numbers to simulate a random
sample of the players. (Lesson 10.3)
A list of 20 randomly generated numbers representing MP3 players is:
77
19
101
67
156
5
378
191
188
124
116
226
458
496
333
161
a. Let numbers 1 to 25 represent players that are
.
b. Let numbers 21 to 500 represent players that are
.
c. How many players in this sample are expected to be
defective?
d. If 300 players are chosen at random from the shipment, how
many are expected to be defective based on the sample? Does
the sample provide a reasonable inference? Explain.
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230
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Unit 5
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474
78
MODULE
MODULE
?
11
Analyzing and Comparing
Data
Key Vocabulary
mean absolute deviation
(MAD) (desviación
absoluta media, (DAM))
ESSENTIAL QUESTION
How can you solve problems by analyzing and comparing data?
EXAMPLE
The box plots show amounts donated
to two charities at a fundraising drive.
Compare the shapes, centers and
spreads of the box plots.
Charity A
Charity B
8 12 16 20 24 28 32 36 40 44 48 52
Shapes: The lengths of the boxes and
overall plot lengths are fairly similar, but while the whiskers for Charity A are
similar in length, Charity B has a very short whisker and a very long whisker.
Centers: The median for Charity A is $40, and for Charity B is $20.
Spreads: The interquartile range for Charity A is 44 - 32 = 12. The
interquartile range for Charity B is slightly less, 24 - 14 = 10.
The donations varied more for Charity B and were lower overall.
EXERCISES
The dot plots show the number
of hours a group of students
spends online each week, and
how many hours they spend
reading. (Lesson 11.1)
0 1 2 3 4 5 6 7
Time Online (h)
0 1 2 3 4 5 6 7
Time Reading (h)
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1. Calculate the medians and ranges of the dot plots.
2. The average times (in minutes) a group of students spends studying
and watching TV per school day are given. (Lesson 11.3)
Studying:
Watching TV:
25, 30, 35, 45, 60, 60, 70, 75
0, 35, 35, 45, 50, 50, 70, 75
a. Find the mean times for studying and for watching TV.
b. Find the mean absolute deviations (MADs) for each data set.
c. Find the difference of the means as a multiple of the MAD, to two
decimal places.
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357
Unit
Project
7.RP.2c, 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4
A Sample? Simple!
For this project, choose one of the following topics.
Randomly sample at least 25 people and record their
answers to the question you write about the topic.
• Number of pets in a home
• Number of books read optionally in the past 6 months
• Number of cell phone lines a family uses
• Number of full-time or part-time students in a family
• Number of hours of sleep obtained last night
Use your data to create a presentation that includes the
following:
•
•
•
•
MATH IN CAREERS
ACTIVITY
Type A
Entomologist An entomologist is
studying how two different types of flowers
appeal to butterflies. The box-and-whisker
plots show the number of butterflies
7
9
11
13
15
that visited one of two different types of
Number of Butterflies
flowers in a field. The data were collected
over a two-week period, for one hour each day. Find the median, range, and
interquartile range for each data set. If you had to choose one flower as having
the more consistent visits, which would you choose? Explain your reasoning.
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Unit 5
Type B
17
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Radius Images/Corbis
An explanation of how you chose your random sample
The question you asked and the answers you received
A box plot of your data
Your interpretations of the data, including the median, the range, and the
most common items of data
• Your inference, based on your data, of the number of 5,000 randomly
chosen people who would give the answer to your question that your
median group gave
Use the space below to write down any questions you have or
important information from your teacher.